Straightforward intermediate rank tensor product smoothing in mixed models

Tensor product smooths provide the natural way of representing smooth interaction terms in regression models because they are invariant to the units in which the covariates are measured, hence avoiding the need for arbitrary decisions about relative scaling of variables. They would also be the natural way to represent smooth interactions in mixed regression models, but for the fact that the tensor product constructions proposed to date are difficult or impossible to estimate using most standard mixed modelling software. This paper proposes a new approach to the construction of tensor product smooths, which allows the smooth to be written as the sum of some fixed effects and some sets of i.i.d. Gaussian random effects: no previously published construction achieves this. Because of the simplicity of this random effects structure, our construction is useable with almost any flexible mixed modelling software, allowing smooth interaction terms to be readily incorporated into any Generalized Linear Mixed Model. To achieve the computationally convenient separation of smoothing penalties, the construction differs from previous tensor product approaches in the penalties used to control smoothness, but the penalties have the advantage over several alternative approaches of being explicitly interpretable in terms of function shape. Like all tensor product smoothing methods, our approach builds up smooth functions of several variables from marginal smooths of lower dimension, but unlike much of the previous literature we treat the general case in which the marginal smooths can be any quadratically penalized basis expansion, and there can be any number of them. We also point out that the imposition of identifiability constraints on smoothers requires more care in the mixed model setting than it would in a simple additive model setting, and show how to deal with the issue. An interesting side effect of our construction is that an ANOVA-decomposition of the smooth can be read off from the estimates, although this is not our primary focus. We were motivated to undertake this work by applied problems in the analysis of abundance survey data, and two examples of this are presented.     

Adolescent accounts of the UK National Lottery and scratchcards: an analysis using Q-sorts

The study examined adolescents' accounts of the UK National Lottery and scratchcards. Q-sorts were used to examine the views of 62 participants aged between 11 and 15 years of age. Findings identified four distinct accounts in relation to the National Lottery (Moral Opposition, Luck Seeking, Rationalist, & Uncertainty), and four distinct accounts in relation to scratchcards (Scepticism, Thrill-Seeking, Rationalist, & Libertarian). Some of the accounts identified described the UK National Lottery and scratchcards as bona fide forms of gambling. Reports indicated that adolescents were pessimistic about the chances of winning large sums of money, while other accounts demonstrated gambling misperceptions particularly in relation to their belief in luck and the laws of probability. It is argued that to fully understand why adolescents take part in these activities it is important to consider the diverse ways that adolescents represent these activities. These differing representations will have consequences for measures aimed at reducing, preventing, or treating adolescent problem gambling. The utility of Q-sorts as a technique for examining the views of problem and non-problem gamblers is also discussed.     

On tests for normality of experimental error in ridge regression

Considered are tests for normality of the errors in ridge regression. If an intercept is included in the model, it is shown that test statistics based on the empirical distribution function of the ridge residuals have the same limiting distribution as in the one-sample test for normality with estimated mean and variance. The result holds with weak assumptions on the behavior of the independent variables; asymptotic normality of the ridge estimator is not required.     

466 AND ALL THAT

This paper describes a complex long-term citrus experiment conducted at Griffith, New South Wales, over a period of 35 years. The design has a number of interesting features. Information on certain interactions is spread over several strata of the analysis of variance and the addition of new treatment factors, in 1955 and 1971 raised difficult problems.     

A randomized test of a small-group interactive social norms intervention

Social norms interventions are a common approach to addressing the problem of college student drinking. An increasingly popular but not yet well-validated social-norms-based intervention consists of providing normative feedback to students in small groups. OBJECTIVE, PARTICIPANTS, AND METHODS: In this study, the authors used a randomized design to test an interactive form of small-group social norms correction with 502 first-year students during September and October 2001. Because the unit of random assignment was at the level of the classroom, the authors used hierarchical linear modeling to estimate variability. They investigated whether small-group interactive social norms correction could influence alcohol perceptions and behaviors above and beyond a noninteractive social norms education approach. RESULTS: Results indicate that the approach has a fairly substantial influence on student perceptions; however, the findings do not support an influence of interactive small-group social norms correction on measures of alcohol use behaviors. CONCLUSIONS: Given these findings, the use of interactive small-group social norms approach to influence student misperceptions may be considered as a primer for population-level preventive interventions.     

Understanding Attachment Transitions Through the Lived Experiences of Young Black Gay and Bisexual Men

We conducted a mixed-methods study to identify factors that influence transitions in attachment style between childhood and adulthood among 28 young Black gay and bisexual men (YBGBM) in the United States. We used a phenomenological approach to data integration, with the major component to the results being garnered from the qualitative interviews. We organized our results by four attachment transition groups: stable secure (secure attachment in childhood and young adulthood), stable insecure (insecure attachment in childhood and young adulthood), secure to insecure (secure in childhood and insecure in adulthood) and insecure to secure (insecure in childhood and secure in adulthood). Within each of the typologies, two major themes emerged: social support and religion. Generally, transitions from secure to insecure attachment were related to experiences of perceived rejection by a parental figure during adolescence that corresponded with sexual orientation disclosure. Transitions from insecure to secure attachment appeared to be related to the absence of an attachment figure early in life, but with the acquisition of an attachment figure during early to late adolescence. The findings from our study suggest a need for attachment-based approaches to social support interventions, as well as for an increased understanding of social and cultural factors that impact attachment changes among practitioners who use attachment-based therapy models for YBGBM.     

Ideological group influence: central role of message meaning

Social influence, in Asch’s famous analysis, depends on recipients’ interpretations of what issues mean. Building on this view, we showed that influence is a two-step process in which recipients first infer the meaning of a message based on the ideology of the source group. In the second step, recipients agree more with messages that support their own group ideologies. Supporting the causal sequence in the model, recipients’ attitudes changed when message meaning changed, but not when message meaning was held constant.